Two of the most important power quality problems facing industrial customers of electrical power utilities are voltage sags and voltage interruptions. A voltage sag is a momentary (i.e., 0.5-30 cycle) decrease in the RMS voltage magnitude provided to the customer. Voltage interruptions occur when a protective device actually interrupts the power provided to a particular customer. Voltage interruptions will normally only occur if there is a fault on the particular circuit that is being interrupted. Voltage sags, however, may occur during the period of a fault for faults over a wide part of a power system network. Faults on parallel feeder circuits or on remote parts of a power transmission system will cause voltage sags in many parts of the power system, but typically will not result in actual voltage interruptions. Voltage sags are thus much more frequent than voltage interruptions. For equipment that is sensitive to voltage sags, the frequency of problems resulting from voltage sags will be much greater than that resulting from complete voltage interruptions.
Faults resulting in voltage sags can occur within a particular customer's plant, or in the utility system providing power to the customer's plant. The voltage sag condition will last until the fault is cleared by a protective device. In the plant, this will typically be a fuse or a plant feeder breaker. On the utility system, the fault could be cleared by a branch fuse or a substation breaker. If reclosing is used by the utility, the voltage sag condition can occur multiple times.
Utility system faults can occur on the distribution system or on the transmission system. The typical distribution system includes a number of parallel feeders supplied from a common bus. A fault on one of the feeders will cause a voltage interruption on that feeder, which will directly affect the customer on that feeder. All of the customers on parallel feeders will experience a voltage sag while the fault is actually on the system. With the reclosing breakers at the substation, customers on parallel feeders can experience several voltage sags in succession, each lasting for durations ranging from a couple of cycles to more than ten cycles. Utility system faults on the transmission system can affect even more customers. Customers hundreds of miles from the fault location can experience a voltage sag when the fault is on the transmission system, resulting in equipment misoperation.
The large majority of faults on a utility system are single line-to-ground faults (SLGF). Three-phase faults are more severe, but less common. SLGFs often result from weather conditions such as lightning, wind, and ice. Contamination of insulators, animal contact, and accidents involving construction or transportation activities also cause such faults. Although utilities go to great lengths to prevent such faults on the system, they cannot be eliminated completely.
When a SLGF occurs, the voltage on the faulted phase goes to zero at the fault location. The voltage at the substation and on parallel feeders will depend on the distance of the fault from the substation. On transmission systems, the phase voltage at remote locations from the fault depends on the overall network impedances.
The quantity of concern to utility customers is the voltage level at the customer bus resulting from an SLGF somewhere on the utility system. The customer bus voltage will depend on the transformer connections between the faulted system and the customer bus. For a distribution system fault, the worst case occurs when the fault is close to the substation bus. Effectively, this is the same as a fault near the customer transformer primary. It is important to note that even a SLGF on the primary winding of the customer transformer will typically not result in a zero voltage across any of the secondary windings. For example, for an SLGF on the primary winding of a wye grounded/delta transformer, a circulating fault current in the delta secondary winding results in a voltage on each winding. With such a customer transformer connection, an SLGF on the primary of the transformer will result in a voltage sag at the customer bus that is no lower than 33% of the normal value.
SLGFs resulting in voltage sags, but without causing complete voltage interruptions, account for the great majority of faults on a utility power system.
However, statistics of voltage disturbances show that the vast majority of voltage sags are within 40% of the normal voltage level, and last less than 10 cycles.
Various types of electrical devices can be affected by even modest amounts of voltage sag. Such devices include motors, adjustable-speed drives, high-intensity discharge lighting, and control devices such as computers, contactors, and programmable logic controllers. The voltages experienced during a voltage sag condition will depend on the equipment connection. Individual phase voltages and phase-to-phase voltages can be quite different during an SLGF condition on the utility system. Thus, some single phase loads may be unaffected during the voltage sag condition, while other single phase loads may drop out, even though their sensitivities to voltage sags may be identical. Voltage unbalance is also a concern for motor heating. However, the durations of the unbalanced voltages during fault conditions are so short that motor heating is typically not a significant concern. Different categories of equipment, and even different brands of equipment within a category, can have significantly different sensitivities to voltage sags. It is important to recognize than an entire industrial process can depend on the sensitivity of a single piece of equipment. The overall process may involve controls, drives, motor contactors, robotics, etc., that are all integral to the plant operation. The failure of a single piece of equipment due to a voltage sag can, therefore, cause an entire industrial process to shut down. The interruption of an industrial process due to a voltage sag can result in very substantial costs to the operation. These costs include lost productivity, labor costs for clean-up and restart, damaged product, reduced product quality, delays in delivery, and reduced customer satisfaction.
Various solutions to the voltage sag problem have been suggested. It is possible for utilities to reduce the number of faults on the utility system through design practices and additional equipment, but it is never possible to eliminate faults on the system. Industrial plant equipment may be designed to handle the most common voltage sag conditions, or be retrofitted with appropriate power conditioning to ride through the voltage sag condition. Power conditioning equipment may be provided for particularly sensitive loads. Many voltage sag conditions can be handled by ferroresonant, or constant voltage, transformers. Such transformers may be effective power conditioners for loads with relatively low power requirements and loads which are constant. High power and variable loads pose a problem for such transformers because of the tuned circuit on the transformer output. Moreover, such transformers are heavy, expensive, and difficult to design and construct.
Another method for compensating voltage sags caused by faults in a utility power system involves the injection of energy into the power system transmission line to restore the load voltage magnitude. This may be accomplished by connecting an inverter in series with the transmission line. A DC power source, such as a battery, superconducting magnetic energy storage device, or a large DC bus capacitor, is used to provide power to the inverter. The inverter is controlled to convert the DC power provided by the DC power source into a voltage waveform which is injected into the transmission line to compensate for the voltage sag to restore the load voltage to the pre-fault load voltage condition. Since, in such systems, energy is provided from the DC power source to the utility transmission line, sufficient power must be stored in the DC power source to provide for voltage sag compensation throughout the duration of a fault on the utility system.
Other power quality problems which are also faced by industrial customers include unbalanced multi-phase power, which may be caused by unbalanced loads connected to the power system, and harmonic distortion in the power supply line, which is typically caused by non-linear loads, such as three-phase diode and thyristor bridge inverters used in DC power supplies, adjustable speed drives (ASDs), and Uninterruptible Power Supplies (UPS), which cause harmonic distortion in the power supply by injecting harmonic current into the power system that generates transient and spurious frequencies in the power signal. Active power line conditioners and/or active filters may be used to compensate for such unbalanced load and harmonic distortion conditions. Active line conditioners/balancers and harmonic filters may be implemented using inverters connected in series and/or in parallel with the power system transmission lines supplying the load. The inverters are controlled to inject or withdraw energy from the transmission line at the desired frequency to compensate for the unbalanced load and/or harmonic distortion condition.
Control of active power line conditioners and active harmonic filter inverters is often accomplished using a synchronous reference frame (SRF) based controller. An SRF based controller receives measure voltages or currents in the three-phase a-b-c reference frame as inputs, and transforms the three-phase quantities into a synchronously rotating two-phase d-q reference frame. Inverter control signals are generated initially from the measured quantities in the two-phase synchronous reference frame, and then converted back to the three-phase reference frame to be applied to control the inverter.
The transformation from a three-phase reference frame to a synchronously rotating two-phase reference frame is illustrated in FIG. 1. For exemplification purposes, the three-phase quantities may be three-phase currents i.sub.a, i.sub.b, and i.sub.c. The transformation of the three-phase currents i.sub.a, i.sub.b, and i.sub.c into synchronously rotating two-phase currents i.sup.e.sub.q and i.sup.e.sub.d is a two-step process. First, the three-phase currents are transformed to a two-phase ds-qs reference frame that is stationary with respect to the three-phase system. This three-phase to two-phase stationary transformation is equivalent to a set of linear equations with constant coefficients, as shown in FIG. 1. The two-phase stationary currents i.sup.s.sub.q and i.sup.s.sub.d are vectors that are 90.degree. out of phase with each other. This three-phase to stationary two-phase transformation may be accomplished by a conventional three-phase to two-phase stationary transformation device 40 which executes the following equation: ##EQU1## where k.sub.1 is a constant value equal to .sqroot.(2/3). The second step of the three-phase to two-phase synchronous reference frame transformation is the transformation of the stationary two-phase reference frame quantities ds and qs into synchronous rotating reference frame quantities de and qe. This stationary to rotating transformation 41 is achieved by multiplying the stationary reference frame values ds and qs by unit vectors cos .theta. and sin .theta.. Transformation from the stationary to rotating two-phase reference frame is accomplished by execution of the following equation: ##EQU2## The rotation transformation is often referred to as a "vector rotation", since the d-q quantities can be combined as a vector. The transformation then amounts to the rotation of one vector with respect to another. FIG. 1 includes the vector rotation equations.
The unit vectors cos .theta. and sin .theta. are obtained from a phase-locked loop (PLL). An exemplary prior art PLL is illustrated at 42 in FIG. 2. The PLL obtains an instantaneous vector sum of (for example) the three-phase input voltages (V.sub.ia, V.sub.ib, and V.sub.ic) by using a three-to-two phase transformation 43 that generates signals V.sub.di and V.sub.qi in the synchronously rotating two-phase reference frame. These signals are conveyed to a phase detector 44. The phase detector output may be defined as: EQU sin (phase error)=V.sub.di cos .theta.-V.sub.qi sin .theta..(3)
In equation 3, sin .theta. and cos .theta. are the values presently pointed to in a look-up table 45. The phase detector 44 output is processed by a proportional plus integral (PI) controller 46 that provides a fast response and zero steady-state tracking error. The PI controller 46 is used to determine the count parameter value of a timer or digital oscillator 47. The timer count value is decremented from the count parameter value at a constant rate. When zero is reached, the sin .theta. and cos .theta. pointers in the look-up table 45 are incremented. Since this is a closed-loop system, the count parameter value is either increased or decreased, depending on the PI controller 46 output, so as to reduce the phase error until a phase-locked condition is achieved.
The transformation from a synchronously rotating two-phase de-qe reference frame to a three-phase a-b-c reference frame is illustrated in FIG. 3. A rotating to stationary transformation 48 first transforms rotating two-phase quantities, for example, voltages V.sub.d.sup.e and V.sub.q.sup.e, to stationary two-phase values using the equation: ##EQU3## where cos .theta. and sin .theta. are derived from a PLL. The resulting stationary two-phase values V.sup.s.sub.d and V.sup.s.sub.q are then transformed by a stationary two-phase to three-phase transformation 49 to three-phase voltage quantities using: ##EQU4## The vector rotation equations for the two-phase to three-phase transformations are also presented in FIG. 3.